Implications

We have the following indirect implication of form equivalence classes:

22 \(\Rightarrow\) 26
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
22 \(\Rightarrow\) 26 clear

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number Statement
22:

\(UT(2^{\aleph_{0}},2^{\aleph_{0}},2^{\aleph_{0}})\): If every member of an infinite  set of cardinality \(2^{\aleph _{0}}\) has power \(2^{\aleph_{0}}\), then the union has power \(2^{\aleph_{0}}\).

26:

\(UT(\aleph_{0},2^{\aleph_{0}},2^{\aleph_{0}})\): The union of denumerably many sets each of power \(2^{\aleph _{0}}\) has power \(2^{\aleph_{0}}\).

Comment:

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